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2006 Non-uniform dependence on initial data for a family of non-linear evolution equations
Erika A. Olson
Differential Integral Equations 19(10): 1081-1102 (2006).

Abstract

We show that solutions to the periodic Cauchy problem for a family of non-linear evolution equations, which contains the Camassa-Holm equation, do not depend uniformly continuously on initial data in the Sobolev space $H^s(\mathbb{T})$, when $s=1$ or $s\geq 2$.

Citation

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Erika A. Olson. "Non-uniform dependence on initial data for a family of non-linear evolution equations." Differential Integral Equations 19 (10) 1081 - 1102, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35426
MathSciNet: MR2278671

Subjects:
Primary: 35Q53
Secondary: 35B10 , 35B35

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 10 • 2006
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